3 Unit Conversions

Introduction:

In this module you will learn several ways to convert units of length within and between the imperial and metric (S.I.) systems.

Chapter Contents:

• Topic 1: S.I. and Imperial Units of Measure
  • 1.1 Units of Length
  • 1.2 The Metric System
  • 1.3 Metric System Unit Conversion
• Topic 2: Converting Units using the Proportion Equation
• Topic 3: Converting Units using Unit Analysis
• Test: Outcome 3

Topic 1: S.I. and Imperial Units of Measure

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There are two systems when it comes to measurement. In the United States, and in some cases unofficially in Canada, the Imperial or Standard system of measurement is used. In Canada and the rest of the world, the S.I. (Système International) or Metric system is used.

1.1 Units of Length

Here is a listing of common units of measure in the metric system and the imperial system listed in order from smallest to largest.

Metric	Imperial
Millimetre (mm)
Centimetre (cm)
	Inch (in)
	Foot (ft)
	Yard (yd)
Meter (m)
Kilometer (km)
	Mile (mi)

1.2 The Metric System

The metric system has a base unit for each type of measurement:

Base Unit	Quantity
Meter (m)	Length
Liter (L)	Volume
Gram (g)	Mass
Second (s)	Time
Degree Celsius (˚C)	Temperature

In order to make the unit larger or smaller it is multiplied or divided by factors of 10. Each multiple of 10 has a name. Here are some common multipliers and names:

Name	Multiplier
Mega (M)	X 1,000,000 (one million)
Kilo (k)	X 1,000 (one thousand)
Centi (c)	X 0.01 (one hundredth) (or÷100)
Milli (m)	X 0.001 (one thousandth) or (÷1,000)

Note: the word “metre” is spelled with the -re ending everywhere except the United States, where it is spelled with -er. A meter is something you plug change into for parking.

1.3 Metric System Unit Conversion

You cannot convert between base units. For example, metres cannot be converted to grams or seconds cannot be converted to degrees Celsius.

Within each base unit you can use the prefixes (multipliers) to create larger or smaller units. For example, one kilogram is one thousand times larger than a gram. One milligram is one thousandth the size of a gram.

What makes the metric system so easy to deal with is that the name of the multiplier tells you what the conversion factor is. Converting units is just a matter of moving the decimal place an appropriate number of spots. This picture is sometimes used to remember how many decimal places to move.

 

To use the chart, start at the prefix you have. Move to the left or right to the prefix you want. The number of spots you move is the number of decimal places you must move. The direction you move on the chart is the direction you move the decimal.

Example 1

Convert the following metric measurements:

• 34 millimetres to centimetres.

• Convert 2.3 kilometres to centimetres.

• Convert 350 milligrams to grams.

Grams are the base unit for mass, but the system works the same as for length.

1.1 – 1.3Practice Exercises: S.I. and Imperial Units of Measure

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Topic 2: Converting Units using the Proportion Equation

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There are not many things you should memorize in math. This, however, is one of them. Memorize the conversion factors that are highlighted in yellow, and your life will be a lot easier when it comes to converting measurements. You don’t need to memorize all the unit conversions. If you know the basic ones you can convert any units by using several steps.

Example 1

Convert 23.6 inches to millimeters

From the above table of conversions, we know that 1 inch = 25.4 millimeters. This can be written as a rate. There are 25.4 millimeters per inch or. When setting up the proportion equation always put the same units on top and the same units on bottom. It doesn’t matter which goes on top (inches or millimeters) they just have to be the same on both sides:I am trying to figure out how many millimeters there are in one inch, so I am letting the variable “x” represent that amount.

Solve the proportion equation by cross multiplying and dividing by the third number.

Practice Exercises: Converting Units Using the Proportion Equation

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Topic 3: Converting Units using Unit Analysis 

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Another convenient way of converting units is using “unit analysis.” This is particularly convenient if we need to convert units where several steps are involved. In this method, units that are the same on top of the fraction as they are on the bottom get crossed off. Whatever is left is the unit that you end up with.

Example 1

Convert 4.76 yards to metres.

If you can remember that 1 metre is roughly 1.09361 yards, you can calculate this in one step. I am encouraging you NOT to memorize this, but to use the basic conversions highlighted in yellow and do the conversion with multiple steps. (This being said, this is the unit conversion with the most steps, so it may be useful to memorize that 1 metre is roughly 1.09 yards.)

• Create a roadmap using conversions you know:

yards ⇒ feet ⇒ inches ⇒ millimetres ⇒ metres

• Start with 4.76 yards and multiply all the unit conversions as rates

• Cross off pairs of units that are the same on top and bottom

• The calculation can be done by multiplying or dividing all the conversion factors. If the conversion factor is “on top” of the fraction, multiply. If the conversion factor is on the bottom, you divide.

Practice Exercises: Converting Units by Unit Analysis

1. Convert the following units using unit analysis

a) 36.5 inches to mm

b) 2.378 feet to mm

c) 18.4 inches to yards

d) 4.35 metres to feet

e) 18.497 yards to metres

 

Practice Exercises Solutions:

a) 927.1 mm

b) 725 mm

c) 0.51 yards

d) 14.27 feet

e) 16.91 metres

2. Locate the measurements on the ruler below.

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Review Exercises: Converting Within and Across Measurement Systems

Use the following table of conversions to do the conversions:

 

1. How many yards are in 10 meters?

2. How many kilometers are in 1 mile?

3. How many centimeters are in 5 feet?

4. How many feet are in 154 centimeters?

5. How many centimeters are in 8 inches?

6. How many meters are in 8 feet?

7. How many meters are in 3 yards

8. How many feet are in 2 meters?

9. How many inches are in 9 centimeters?

10. How many miles are in 7 kilometers?

 

Review Exercises Solutions:

1. 10.94 yards
2. 1.609 km
3. 152.4 cm
4. 5.0512 ft
5. 20.32 cm
6. 2.4384 m
7. 2.742 m
8. 6.562 ft
9. 3.546 in
10. 4.347 miles

Outcome 3 Test 

Complete the Essentials 1 Math: Unit Conversions Chapter Quiz on Brightspace.